Set Partitions Iterator

Transcription

1 Set Partitions Iterator Patrick Stein March 26, 2008 Contents 1 The set-partition-iterator class Packaging Slots Constructor Get Partition Next Partition Test Code partitions.lisp partitions-tests.lisp List of Noweb Chunks 5 Noweb Defintions 5 1 The set-partition-iterator class After a few false starts, I stumbled upon a paper titled: Efficient Generatof of Set Partitions by Michael Orlov 1 The code here, as an initial cut, fairly directly follows the algorithms presented in that paper. They are written iteratively, so they won t be as spiffy-lispy as one might hope. Where I see ways to easily adapt, I will. We re going to define a class called set-partition-iterator. 1 set-partition-iterator declaration 1 (4c) (defclass set-partition-iterator () ( set-partition-iterator slot declarations 2f )) set-partition-iterator, used in chunks

2 March 26, We are going to give it a method to query the current partition. 2a set-partition-iterator get-partition declaration 2a (4c) (defgeneric get-partition (iter) (:documentation "Retrieve the current partition from a partition iterator")) get-partition, used in chunks 2 4. We also need a method to advance to the next partition. 2b set-partition-iterator next-partition declaration 2b (4c) (defgeneric next-partition (iter) (:documentation "Advance the iterator to the next partition")) next-partition, used in chunks 2c and Packaging To keep the namespace somewhat clean, we re going to put this stuff in its own package. 2c set-partition-iterator package declaration 2c (4c) (defpackage :com.nklein.set-partition-iterator (:use :common-lisp) (:export :set-partition-iterator :get-partition :next-partition)) Uses get-partition 2a, next-partition 2b, and set-partition-iterator 1. 2d set-partition-iterator package 2d (4c) (in-package :com.nklein.set-partition-iterator) 2e set-partition-iterator package load 2e (load "partitions.fasl") 1.2 Slots We need a slot to keep track of the list we are trying to partition. 2f set-partition-iterator slot declarations 2f (1) 2g (real-list :initarg :list) set-partition-iterator::real-list, never used. We need a slot to keep track of the partitioning information. Keeping with the referenced paper, I will call this state kappa. 2g set-partition-iterator slot declarations 2f + (1) 2f 3a kappa set-partition-iterator::kappa, never used.

3 March 26, And, we need a slot to keep track of the current maximum partition information. In keeping with the referenced paper, I will call this state MM. 3a set-partition-iterator slot declarations 2f + (1) 2g MM set-partition-iterator::mm, never used. 1.3 Constructor After the initialize-instance method provides the list, we re going to copy the list so that we don t have to worry about the caller destroying the list. After that, we are going to prepare the first partitioning state. 3b set-partition-iterator constructor 3b (4c) (defmethod initialize-instance :after ((iter set-partition-iterator) &key) (let ((len (length real-list))) paritition-iterator constructor copy real-list 3c paritition-iterator constructor prepare kappa and MM 3d ))) Copying the list is quite straightforward except that we reverse it just so that our output looks nicer. 3c paritition-iterator constructor copy real-list 3c (3b) (setf real-list (reverse real-list)) And, there s not much work to do to initialize the kappa and MM states. 3d paritition-iterator constructor prepare kappa and MM 3d (3b) (setf kappa (make-array len :initial-element 0)) (setf MM (make-array len :initial-element 0)) 1.4 Get Partition 3e set-partition-iterator get-partition 3e (4c) (defmethod get-partition ((iter set-partition-iterator)) (let ((ret (make-array (+ (reduce # max MM) 1) :initial-element nil)) (len (length kappa))) set-partition-iterator get-partition fill in ret 3f ret))) Uses get-partition 2a and set-partition-iterator 1. 3f set-partition-iterator get-partition fill in ret 3f (3e) (dotimes (ii len) (push (elt real-list ii) (elt ret (elt kappa ii))))

4 March 26, Next Partition 4a set-partition-iterator next-partition 4a (4c) (defmethod next-partition ((iter set-partition-iterator)) (let ((len (length kappa)) (k0 (elt kappa 0))) (do ((ii (- len 1) (1- ii))) ((<= ii 0)) (let ((ki (elt kappa ii)) (mi1 (elt MM (- ii 1)))) (when (<= ki mi1) (setf (elt kappa ii) (+ ki 1)) (setf (elt MM ii) (max (elt MM ii) (elt kappa ii))) (let ((mi (elt MM ii))) (do ((jj (+ ii 1) (1+ jj))) ((>= jj len)) (setf (elt kappa jj) k0) (setf (elt MM jj) mi))) ; (format t "kappa = ~a~%" kappa); ; (format t "MM = ~a~%" MM); (return-from next-partition (get-partition iter))))))) nil) Uses get-partition 2a, next-partition 2b, and set-partition-iterator Test Code 4b partitions-tests test code 4b (5b) (let ((foo (make-instance set-partition-iterator :list (:a :b :c :d)))) (do ((pp (get-partition foo) (next-partition foo)) (cntr 1 (1+ cntr))) ((not pp) cntr) (format t "~a: ~a~%" cntr pp))) Uses get-partition 2a and next-partition 2b. 4c 1.7 partitions.lisp partitions.lisp* 4c set-partition-iterator package declaration 2c set-partition-iterator package 2d set-partition-iterator declaration 1 set-partition-iterator constructor 3b set-partition-iterator get-partition declaration 2a set-partition-iterator get-partition 3e set-partition-iterator next-partition declaration 2b set-partition-iterator next-partition 4a

5 March 26, partitions-tests.lisp 5a partitions-tests package declaration 5a (5b) (defpackage :com.nklein.set-partition-iterator.test (:use :common-lisp :com.nklein.set-partition-iterator)) (in-package :com.nklein.set-partition-iterator.test) 5b partitions-tests.lisp* 5b partitions-tests package declaration 5a partitions-tests test code 4b List of Noweb Chunks paritition-iterator constructor copy real-list 3c 3b, 3c paritition-iterator constructor prepare kappa and MM 3d 3b, 3d partitions-tests package declaration 5a 5a, 5b partitions-tests test code 4b 4b, 5b partitions-tests.lisp* 5b 5b partitions.lisp* 4c 4c set-partition-iterator constructor 3b 3b, 4c set-partition-iterator declaration 1 1, 4c set-partition-iterator get-partition 3e 3e, 4c set-partition-iterator get-partition declaration 2a 2a, 4c set-partition-iterator get-partition fill in ret 3f 3e, 3f set-partition-iterator next-partition 4a 4a, 4c set-partition-iterator next-partition declaration 2b 2b, 4c set-partition-iterator package 2d 2d, 4c set-partition-iterator package declaration 2c 2c, 4c set-partition-iterator package load 2e 2e set-partition-iterator slot declarations 2f 1, 2f, 2g, 3a Noweb Definitions get-partition: 2a, 2c, 3e, 4a, 4b next-partition: 2b, 2c, 4a, 4b set-partition-iterator: 1, 2c, 2d, 3b, 3e, 4a, 5a set-partition-iterator::kappa: 2g set-partition-iterator::mm: 3a set-partition-iterator::real-list: 2f